Enhancing the NIR Photocurrent in Single GaAs Nanowires with Radial p-i-n Junctions by Uniaxial Strain

III–V compound nanowires have electrical and optical properties suitable for a wide range of applications, including photovoltaics and photodetectors. Furthermore, their elastic nature allows the use of strain engineering to enhance their performance. Here we have investigated the effect of mechanical strain on the photocurrent and the electrical properties of single GaAs nanowires with radial p-i-n junctions, using a nanoprobing setup. A uniaxial tensile strain of 3% resulted in an increase in photocurrent by more than a factor of 4 during NIR illumination. This effect is attributed to a decrease of 0.2 eV in nanowire bandgap energy, revealed by analysis of the current–voltage characteristics as a function of strain. This analysis also shows how other properties are affected by the strain, including the nanowire resistance. Furthermore, electron-beam-induced current maps show that the charge collection efficiency within the nanowire is unaffected by strain measured up to 0.9%.


S1. Theoretical model for analysis of dark I-V characteristics
The electrical circuit that was used to model the nanowire-contact system is shown in Figure   1. In this configuration, a positive applied bias corresponds to a forward biased p-n diode and a reversed biased Schottky diode. The current through the p-n diode, , is described 1 by the single diode model for a non-ideal solar cell [1], where is the voltage drop over , is the diode saturation current, is the diode 1 1 ideality factor, is the elementary charge, is Boltzmann's constant and is the temperature. Applying Kirchhoff's law to the model circuit, we then have an expression for the total current, , and for the applied bias, , where , and are the voltage drops over the , and , respectively and is the photogenerated current. In the low bias regime, the current through the reversed ℎ biased Schottky diode, is negligibly small and the contact can be regarded as only a 2 , resistance, . Combining (1), (2) and (3) we get the following expression for as a function of applied bias, in the low bias regime: Supporting information Here and is the Lambert W function. In the high bias regime, the voltage drop = over the Schottky diode will be sufficient for thermionic field emission to occur, resulting in a significant current through the contact even though the Schottky barrier is reversely biased.
According to thermionic field emission theory [2,3], the current through the diode is , where is the Schottky barrier height and with . is the doping concentration of the semiconductor, is the effective electron mass and is * the permittivity of the nanowire. The saturation current for the Schottky diode, can be , expressed as:

Supporting information
Here is the contact area, the effective Richardson's constant and is the difference * between the Fermi energy and the bottom of the conduction band. Solving (2), (3) and (5) numerically, it is possible to calculate the total current as a function of applied voltage also in the high bias regime.

S2. Dark I-V measurements on Nanowire 3
A third nanowire was contacted with the STM-probe in the same manner as described in the main article. Dark I-V measurements were performed at different strain levels, and the parameters , , , , and were extracted by data-fitting. When going from low ℎ to high strain, all the parameters follow the same trends as Nanowire 1 described in Figure 2 in the main article.
Supporting information Figure S2: (a-b) Dark I-V characteristics of Nanowire 3 at different strain levels in the high and low bias regimes, respectively. (c-h) shows , , , , and as a function of ℎ ℎ applied tensile strain, respectively. The values are extracted from the data-fitting.

S3. Illuminated I-V measurements on Nanowire 3
Nanowire 3 was also illuminated by the NIR LED during the straining. The increases with increasing strain, but not as much as in Nanowire 1. One explanation for this is that the shape of the STM-probe varied between the measurements, since it is produced by mechanically cutting a gold wire with a pair of scissors. The STM-probe may partly block the incoming LED light, and the area of the blocked part may thus change whenever a new STMprobe is used. The flattening out of the curve is not observed because the maximum strain reached is lower than for Nanowire 1. Both in Nanowire 1 and Nanowire 3, the is nonzero even without any applied strain. Assuming that the band gap energy of the unstrained nanowire is close to the tabulated value for bulk GaAs (1.42 eV), almost no part of the LED spectrum can be absorbed in the nanowire when no strain is applied. The nonzero is therefore assumed to originate from electron-hole pairs generated in the Si substrate, which diffuse into the nanowires and are separated by the p-i-n junction. The of Nanowire 3 decreases as a function of strain. The reason that there is no increase at moderate strain levels is probably because the increase in is smaller than for Nanowire 1.
The fill factor also decreases with increasing strain, which is most likely a consequence of the decrease in . , and fill factor for Nanowire 3 as a function of strain.

S4. Dark I-V measurements on unmilled Nanowire 4
I-V measurements at different strain levels were performed on a fourth nanowire, Nanowire 4. The difference here is that this nanowire was not milled with the FIB before depositing the Pt creating the contact between the nanowire and the STM-probe. The native oxide layer covering the surface of the nanowire was therefore still intact, acting as a thin insulating layer, making the electrical contact worse. This can be seen by noting that a higher bias was needed to reach the same current compared to the milled Nanowire 1, see Figure 2 (a) and (b). Otherwise, the I-V characteristics of the milled Nanowire 1 and the unmilled Nanowire 4 were very similar. In particular, at low strain there was a distinct current rectification in both wires, caused by the p-i-n junction. The fact that there was a current rectification behavior in the milled Nanowire 1 shows that the FIB milling did not harm the p-i-n junction in the nanowire. Figure S4: (a-b) Dark I-V characteristics of Nanowire 4 at different strain levels in the high and low bias regimes, respectively.

S5. Illuminated I-V measurements on unmilled Nanowire 4
I-V measurements during NIR LED illumination at different strain levels were also performed on the unmilled Nanowire 4. In Nanowire 4 the , and fill factor followed the same trends as in Nanowire 1 as the strain was increased, which shows that the FIB-milling of Nanowire 1 did not influence the strain effect of its photovoltaic behavior. The and of Nanowire 4 reached higher values than Nanowire 1, which is again likely due to the fact that a differently shaped STM-probe was used, in this case assumingly blocking a lesser part , and fill factor for Nanowire 4 as a function of strain.

S6. Videos showing the straining of Nanowire 1-4
The SEM micrographs taken at all the different strain levels for Nanowire 1-4 have been merged into four separate videos. In the videos it can be seen that while the STM-probe is retracted, it also moves irregularly in the lateral directions, giving rise to a small shear component in the strain. However, the maximum lateral movement observed was on the